When does an additional stage improve welfare in centralized assignment?

Dogan, Battal; Yenmez, M. Bumin

Abstract

We study multistage centralized assignment systems to allocate scarce resources based on priorities in the context of school choice. We characterize schools’ capacity-priority profiles under which an additional stage of assignment may improve student welfare when the deferred acceptance algorithm is used at each stage. If the capacity-priority profile is acyclic, then no student prefers any subgame-perfect Nash equilibrium (SPNE) outcome of the 2-stage system to the truthful dominant-strategy equilibrium outcome of the 1-stage system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage system may Pareto dominate the truthful dominant-strategy equilibrium outcome of the 1-stage system. If students are restricted to playing truncation strategies, an additional stage unambiguously improves student welfare: no student prefers the truthful dominant-strategy equilibrium outcome of the 1-stage system to any SPNE outcome of the 2-stage system.

Citation

Dogan, B., & Yenmez, M. B. (2023). When does an additional stage improve welfare in centralized assignment?. Economic Theory, 76, 1145–1173. https://doi.org/10.1007/s00199-023-01488-y

• Journal Article Type: Article
• Acceptance Date: Feb 2, 2023
• Online Publication Date: Feb 24, 2023
• Publication Date: 2023
• Deposit Date: Aug 15, 2023
• Journal: Economic Theory
• Print ISSN: 0938-2259
• Electronic ISSN: 1432-0479
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 76
• Pages: 1145–1173
• DOI: https://doi.org/10.1007/s00199-023-01488-y
• Keywords: Pharmacology (medical)
• Public URL: https://durham-repository.worktribe.com/output/1718222